Description

There are N numbers in a queue.  The origin sequence is from 1 to N. (1 is the head). The operation “Move a b” means to move all the numbers in front of a (including a) and then insert them in front of b without changing order.  Given several such operations and output the final status of the sequence.

Input

There will be only one test case. The test case begins with an integer N indicating the number of people.  There are several operations followed.  The format is “Move a b” (without quote) you can assume that the position of a is in front of the position of b.  The test case is terminated by “Exit” (without quote).

subtask 1 : 1<=N<=100, you can use O(N) algo for each operation.

subtask 2 : 1<=N<=100, you can use O(N) algo for each operation.

subtask 3 : 1<=N<=100000, you need use O(1) algo for each operation.

subtask 4 : 1<=N<=1000000, you need use O(1) algo for each operation.

Output

Output the numbers from the first one to the last one, and separate two consecutive numbers by a space.

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Description

Given a simple, undirected weighted graph G = (V, E, W), output the weight of its minimum spanning tree.

Input

The input includes multiple test cases. The first of the input is an integer T (T <= 1000) specifying the number of test cases. For each case, the first line contains two integers: the number of the node N and the number of the edges M. In the following M lines, each line contains three integers (s_i, e_i, c_i), 1 <= s_i, e_i <= N, 1 <= c_i <= 100, representing the indices of end vertices of an edge and the weight of the edge.

Case 1: 2 <= N <= 10², 1 <= M <= 10³
Case 2: 2 <= N <= 10³, 1 <= M <= 10³
Case 3: 2 <= N <= 10³, 1 <= M <= 10⁴
Case 4: 2 <= N <= 10³, 1 <= M <= 10⁵

Output

For each case, output a single line that indicates the weight of the minimum spanning tree of the graph.

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Description

Given two sets of numbers, output their intersection set.

Input

There are multiple test cases.

Each case contains four lines.

The first line begins with an integer N.

The second line contains N integers, representing the numbers in the first set.

The third line has one integer M, and the fourth line contains M integers, represent the numbers in the second set.

All the numbers are 32 bit signed integers.

The input is terminated if N = 0.

For case 1, 1 <= N, M <= 10³
For case 2, 1 <= N, M <= 10⁴
For case 3, 1 <= N, M <= 10⁵
For case 4, 1 <= N, M <= 10⁶

Output

For each test case, print the intersection of the two sets. Output them in ascending order. If the intersection of the two sets is an empty set, print 「empty」 (without quotes).

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Description

Please compute the sum of two given n-bit binary numbers.

Input

The first line of the input file contains a positive integer t indicating the number of test cases. The first line of each test case is a positive integer n denoting the length of bits. The second and third lines are the two n-bit binary numbers. The first bit of each binary number is always 0, which guarantees that the sum of the two binary numbers can still be expressed as an n-bit binary number.

Case1 : t<=100, n<=100
Case2 : t<=200, n<=1000
Case3 : t<=300, n<=5000
Case4 : t<=400, n<=10000

Output

For each test case, your program should print the sum in the same format as the binary numbers given in input.

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Description

Assume that we need to send a stream of data items as a series of packets. The size limit of a packet is M, and each item i has a size s_i satisfying s_i < M, for i = 1, 2, ....N
For each item i, we can append it to the current packet as long as the total size of the items in the packet does not exceed the limit; otherwise, we put the item into a new packet. 
Our task is to simulate the process and decide how many packets are needed.

Case1: 0<M<=1*10², 0<=N<=20
Case2: 0<M<=2*10⁴, 0<=N<=100
Case3: 0<M<=1*10⁵, 0<=N<=10000
Case4: 0<M<=2*10⁹, 0<=N<=10000

Input

The input consists of several test cases.
Each test case starts with an integer M indicating the size limit of a packet.
The subsequent positive integers enumerate the sizes of the items, and a number 0 denotes the end of the current stream.

Output

The output contains several lines.
Each line prints the number of packets needed to send the stream for the corresponding test case.
Each line is ended with a newline character.

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